http://www.ck12.org Chapter 11. Surface Area and Volume
Guided Practice
- Find the volume of the cone.
- Find the volume of the cone.
- The volume of a cone is 484πcm^3 and the height is 12 cm. What is the radius?
Answers:
- To find the volume, we need the height, so we have to use the Pythagorean Theorem.
52 +h^2 = 152
h^2 = 200
h= 10√
2
Now, we can find the volume.
V=
1
3
( 52 )
(
10
√
2
)
π≈ 370. 24- Use the radius
V=
1
3
π( 32 )( 6 ) = 18 π≈ 56. 55- Plug in what you know to the volume formula.
484 π=1
3
πr^2 ( 12 )
121 =r^2
11 =rPractice
Find the surface area and volume of the right cones. Leave your answers in terms ofπ.
1.
2.
3.ChallengeFind the surface area of the traffic cone with the given information. The gone is cut off at the top (4 inch
cone) and the base is a square with sides of length 24 inches. Round answers to the nearest hundredth.
- Find the area of the entire square. Then, subtract the area of the base of the cone.
- Find the lateral area of the cone portion (include the 4 inch cut off top of the cone).
- Now, subtract the cut-off top of the cone, to only have the lateral area of the cone portion of the traffic cone.
- Combine your answers from #4 and #6 to find the entire surface area of the traffic cone.